Exact Inference for Relational Graphical Models with Interpreted Functions: Lifted Probabilistic Inference Modulo Theories
This work addresses a foundational challenge in AI for probabilistic reasoning, enabling more expressive and efficient inference in relational models, though it builds incrementally on prior frameworks.
The paper tackles the problem of exact probabilistic inference in graphical models with interpreted functions and relations, achieving the first algorithm that efficiently exploits random relations, functions, arithmetic, equalities, and inequalities simultaneously.
Probabilistic Inference Modulo Theories (PIMT) is a recent framework that expands exact inference on graphical models to use richer languages that include arithmetic, equalities, and inequalities on both integers and real numbers. In this paper, we expand PIMT to a lifted version that also processes random functions and relations. This enhancement is achieved by adapting Inversion, a method from Lifted First-Order Probabilistic Inference literature, to also be modulo theories. This results in the first algorithm for exact probabilistic inference that efficiently and simultaneously exploits random relations and functions, arithmetic, equalities and inequalities.